Numerical simulations of cold clumps in the hot accretion flows around black holes

TL;DR

The paper addresses how cold clumps form and evolve inside hot accretion flows around stellar-mass black holes. It employs two-dimensional axisymmetric hydrodynamic simulations with a pseudo-Newtonian potential and bremsstrahlung cooling to track clump evolution, identifying clumps by $T<10^4$ K and $\rho>10^{-5}\rho_{max}$. The key findings show that above a critical accretion rate, clumps form and initially migrate outward due to angular-momentum gains from viscous torque and condensation from larger radii, later fragmenting inward; their centers exhibit quasi-Keplerian motion consistent with weak-coupling expectations. These results enhance understanding of two-phase accretion flows and state transitions in X-ray binaries, and point to future work incorporating magnetic fields and 3D radiative GRMHD models.

Abstract

Previous numerical simulations have shown that cold clumps can form within hot accretion flows, offering insights into the detailed processes of the state transition in black hole X-ray binaries. However, the evolution of the cold clumps has not been investigated in detail yet. In this paper, we conduct hydrodynamic simulations to investigate the evolution of the cold clumps. In addition to previous result that when the accretion rate is high enough the cold clumps emerge within the hot accretion flow, we found that instead of directly moving toward to the black hole, the clumps moves outward when they initially form. The reason should be the combination of viscous torque and the condensation of hot gas from larger radii, which lead to the slightly super-Keplerian angular momentum of the clumps. After reaching the equilibrium position, the clumps begin to fragment at the inner edge with each fragment moving inward sequentially. Generally, the azimuthal movement of the clumps are quasi-Keplerian, being closer to the outer detached Keplerian cold disk rather than the surrounding sub-Keplerian hot accretion flow, which agrees well with the semi-analytical results for weak coupling case in Wang et al. (2012).

Figures (10)

• Figure 1: Initial conditions of the torus for the case $\rho_{\text{max}} =10^{-7}\text{g/cm}^3$. The left, central and right panels correspond to the initial density, temperature and pressure, respectively.
• Figure 2: Time-averaged (from 0.8 $t_g$ to 1.0 $t_g$) radial distributions of mass fluxes of model C3.
• Figure 3: The distribution of density and temperature at different time in Model C1 and C4. The upper two rows display the temperature distribution in simulations C1 and C4, respectively. And the lower two rows show the density distribution. From left to right, the first column shows the time slice at 1.0 $t_g$ before turning on radiative cooling. The second column corresponds to 1.5 $t_g$, and the third column is at 3.0 $t_g$ to show the evolution of accretion after the cooling is turned on.
• Figure 4: The time evolution of mass fraction of the cold clumps and the accretion rate in Simulations C1, C4, B1, B2. The right-vertical axis in each panel represents the ratio of cold gas mass to total mass. The left-vertical axis in each panel represents the black hole accretion rate.
• Figure 5: Radial distribution of mass averaged temperature at different evolutionary times for the models with cold clumps, i.e., Models C5-C8. The characteristic dips in the temperature curves indicate the positions of cold clumps.